The locus of the point P(x, y) satisfying the relation aligned & (x-3)^2+(y-1)^2 & + (x+3)^2+(y-1)^2 =6 is aligned

Step-by-step solution

Given that, aligned & (x-3)^2+(y-1)^2 + (x+3)^2+(y-1)^2 =6 & (x-3)^2+(y-1)^2 =6 aligned - (x+3)^2+(y-1)^2 On squaring both sides, we get aligned (x-3)^2+(y-1)^2 & =36+(x+3)^2+(y-1)^2 & -12 (x+3)^2+(y-1)^2 aligned aligned x^2-6 x & +9+ (y^2-2 y+1 ) = & 36+x^2+6 x+9+y^2-2 y+1 & -12 (x+3)^2+(y-1)^2 aligned (x+3)= (x+3)^2+(y-1)^2 On squaring both sides of above equation aligned & (x+3)^2= [(x+3)^2+(y-1)^2 ] & (y-1)^2=0 aligned Which represents a pair of straight lines.